We present the first general, automated, large-scale analysis of cookie notice compliance. Our method interacts with cookie notices, e.g., by navigating through their settings. It observes declared processing purposes and available consent options using Natural Language Processing and compares them to the actual use of cookies. By virtue of the generality and scale of our analysis, we correct for the selection bias present in previous studies focusing on specific Consent Management Platforms (CMP). We also provide a more general view of the overall compliance picture using a set of 97k websites popular in the EU. We report, in particular, that 65.4% of websites offering a cookie rejection option likely collect user data despite explicit negative consent.